Quantum Electrodynamics on Null Planes and Applications to Lasers
Abstract
The conventional formulation of quantum electrodynamics in which the system develops from one spacelike hyperplane to the next is here replaced by one in which the development proceeds over null hyperplanes. For detailed study a quantized electromagnetic field A^{μ} is chosen to interact with a quantized spin0 particle field Φ in an unquantized electromagnetic field Aextμ as background. If the latter is chosen to be a laser field, the ΦAextμ interaction permits exact closedform solutions (Volkov) and allows the construction of wave packets which cannot be done in the usual formulation. The perturbation solution for the S matrix is therefore conveniently based on the Furry picture. The nullplane formulation has various advantages. In particular, the gauge problem which causes difficulties in the usual theory is absent in the nullplane gauge chosen here. Since there are only two dynamically independent components of A^{μ}, the commutation relations, field equations, gauge conditions, and vacuum definition are all mutually consistent. A natural nullplane gauge is used. Similarities and differences between this and the conventional theory are pointed out. As an application the Compton scattering of a charged particle with a laser beam is shown to lead to an intensitydependent frequency shift. The controversy on this issue is settled here without divergent phase factors, because our wavepacket description permits a clean separation of the particle beam from the laser.
 Publication:

Physical Review D
 Pub Date:
 April 1971
 DOI:
 10.1103/PhysRevD.3.1692
 Bibcode:
 1971PhRvD...3.1692N